Appl. Phys. B 79, 279–283 (2004)
Applied Physics B
DOI: 10.1007/s00340-004-1569-4
Lasers and Optics
s.j.h. petra∗
k.a.h. van leeuwen
l. feenstra∗∗
w. hogervorst
w. vassenu
Atom lithography with two-dimensional
optical masks
Atomic and Laser Physics Group, Laser Centre Vrije Universiteit, De Boelelaan 1081,
1081 HV Amsterdam, The Netherlands
Received: 27 February 2004/Revised version: 25 May 2004
Published online: 29 June 2004 • © Springer-Verlag 2004
ABSTRACT With a two-dimensional (2D) optical mask at
λ = 1083 nm, nanoscale patterns are created for the first time
in an atom lithography process using metastable helium atoms.
The internal energy of the atoms is used to locally damage
a hydrophobic resist layer, which is removed in a wet etching
process. Experiments have been performed with several polarizations for the optical mask, resulting in different intensity
patterns, and corresponding nanoscale structures. The results
for a linear polarized light field show an array of holes with
a diameter of 260 nm, in agreement with a computed pattern.
With a circularly polarized
√ light field a line pattern is observed
with a spacing of λ/ 2 = 766 nm. Simulations taking into
account many possible experimental imperfections can not explain this pattern.
PACS 32.80.Lg;
1
39.25.+k; 81.16.Nd
Introduction
Over the last ten years atomic nanofabrication with
optical masks has been demonstrated in numerous experiments. With a direct deposition technique, 1D structures have
been grown with sodium [1], chromium [2–5], aluminum [6],
ytterbium [7] and iron [8]. Similarly, in a two-step lithography process, experiments have been performed with cesium [9], metastable neon [10, 11], metastable argon [12], and
metastable helium [13]. In a lithography process, a metal film
is covered with an organic resist layer, which is selectively
damaged by the studied atoms. Next, the damaged molecules
and their underlying metal layer are removed with a cyanide
etching solution. Although the lithography procedure requires
an additional step, it has the advantage that the pattern formation does not suffer from atomic diffusion in the growth
process [14], and the structures have no pedestal.
So far, experiments with a 2D optical mask have been
performed by deposition of chromium atoms [15, 16]. Chromium is advantageous because a short wavelength can be used
u Fax: +31-20/4447-999, E-mail: w.vassen@few.vu.nl
∗ Present address: Department of Physics, Umeå University, 90187
Umeå, Sweden
∗∗ Present address: Physikalisches Institut, Universität Heidelberg,
Philosophenweg 12, 69120 Heidelberg, Germany
(λ = 426 nm) implying small structure sizes of 70 – 80 nm.
Disadvantages are the long exposure time and the inevitable
pedestal in the structures. Also, atom lithography with cesium atoms and a holographic light mask has been reported,
resulting in a line pattern with a periodicity of 426 nm and
a perpendicularly superposed line pattern with a 23.4 µm
spacing [17]. We report on experiments with a 2D optical
mask using metastable helium atoms in a lithography procedure. The metastable helium atom has a high internal energy
(20 eV), and the dose of atoms required to affect a single resist molecule is therefore low [18]. This shortens the exposure
time of the samples to about eight minutes [13].
The optical mask is generated by interference of laser
beams that propagate perpendicularly to an atomic beam
which is directed towards the sample. A force is exerted on
the atom by the interaction of the induced atomic dipole moment with the electric field of the standing light wave. For
a two-level atom, the optical potential of the standing-wave
light field can be written as [19]:
I(r)
Γ2
h∆
U(r) =
ln 1 +
,
(1)
2
Isat Γ 2 + 4∆2
where ∆ is the detuning of the light from atomic resonance,
I(r) is the intensity of the light as a function of the position
r = (x, y, z), Isat is the saturation intensity of the optical transition, and Γ is the natural linewidth of the atomic transition.
The dipole force experienced by the atom, corresponding to
this optical potential, is given by:
F(r) = −∇U(r).
(2)
The formation of a 2D optical mask is shown schematically in Fig. 1. The incident light beam, travelling from right
to left in the x -direction, is reflected at 45◦ downward in the
minus y-direction and retro-reflected by the lower mirror. In
this mirror configuration a 2D interference pattern appears
just in front of the upper mirror. The atomic beam propagates in the z -direction through the light field. The samples are
placed in the light field in front of this upper mirror. The two
images of Fig. 1 show the intensity profile of the optical mask
for the two different polarizations used in the experiments.
The left-hand image presents the pattern formed by a linearly
polarized light beam, polarized perpendicular to the plane of
incidence, i.e., in the z -direction. The right-hand image shows
the intensity profile of a circularly polarized light beam.
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Applied Physics B – Lasers and Optics
FIGURE 1 Schematic view of the 2D intensity profiles for linearly polarized light, perpendicular to the plane of incidence (left-hand image) and
circularly polarized light (right-hand image). The mirrors are indicated by the
gray rectangles. The ratio of the wavelength of the light and the waist of the
laser beam is not to scale
2
Experimental setup
The experimental setup is shown in Fig. 2 and is
similar to the setup we described in a previous paper [13].
The helium atoms are transferred to the metastable 2 3 S1
state in a dc helium discharge. The atomic beam is collimated in two dimensions using a curved wavefront technique with converging laser beams [20, 21]. After the 2Dcollimation the transverse velocity spread of the atomic beam,
defined as the full width at 1/ e2 height, is decreased to
3 m/s and the centerline beam intensity is increased sixfold
to 1.1 × 1010 s−1 mm−2 on the sample. The laser light for the
collimation beams is provided by a 20 mW distributed Bragg
reflector diode laser that operates at a wavelength of 1083 nm.
With Doppler-free saturation spectroscopy this laser is ac-
FIGURE 2 Schematic of the setup. Metastable helium atoms are produced
in dc discharge source S and travel in the z-direction toward the sample. In
the collimation section CS, laser beams of diode laser DL allow for collimation of the atomic beam in both x- and y-direction. Part of the diode laser
output (4%) is split of by beam splitter BS for spectroscopy. After reflection by polarizing beam splitter PBS1 and double-passing discharge cell DC
and quarter-wave plate QP1, the light is detected by photodiode PD1. The
light transmitted by PBS1 also passes PBS2 and is analyzed with Fabry–
Perot interferometer FPI and photodiode PD2. The optical standing-wave
mask is made by the fiber laser FL. A small part of its beam reflected by
PBS3 and also analyzed by FPI. For the standing wave the beam is first reflected downward in the y-direction and retro-reflected by the mirror set SW,
which is incorporated in the sample holder inside the vacuum chamber. After
double-passing QP2, the light of the standing wave is reflected by PBS3 and
monitored with power meter PM
tively stabilized to the 2 3 S1 → 2 3 P2 transition of the helium
atom.
The light for the 2D optical mask is obtained from a fiber
laser also operating at a wavelength of 1083 nm and delivering
a power of 800 mW. The frequency of this light is 375 MHz
blue detuned with respect to the 2 3 S1 → 2 3 P2 transition.
The atoms are therefore repelled to the intensity nodes of the
standing-wave light field. The frequency stability of the fiber
laser is monitored with respect to the locked diode laser with
a Fabry–Perot interferometer (see Fig. 2). The laser beam is
focused at the sample holder with a waist (defined as radius at
1/ e2 of the intensity height) of 0.33 mm. The corresponding
Rayleigh length of 32 cm renders the actual focal point uncritical. The maximum saturation parameter is Imax /Isat = 107 ,
where Imax is the maximum intensity at the nodes of the standing wave and Isat = 0.17 mW/cm2 . The retro-reflected laser
beam overlaps the incident beam path over a distance of 3.3 m,
and is then reflected by polarizing beam splitter cube PBS3
and monitored with a power meter. The standing-wave is
aligned with respect to the sample position by first adjusting it
such that it is not clipped by the sample and thus 100% of the
light is back-reflected by the standing-wave mirror onto the
power meter. Next, the beam is displaced by adjusting a micrometer translation stage (not indicated in Fig. 2) and clipped
by the sample until only 50% of the light is back-reflected,
which indicates that the sample position is at the center of
the laser beam. Final fine tuning is done with the translation
stage in order to move the laser beam to the desired position
with respect to the sample. The large distance over which both
the incident and retro-reflected beam overlap reduces the misalignment angle of the laser beam to less than 0.3 mrad. In the
case where a linearly polarized optical mask is used, quarterwave plate QP2 is removed after alignment of the laser beam.
The samples are silicon substrates covered with a 1 nm
chromium layer and a 30 nm gold layer. A hydrophobic resist layer of nonanethiol [CH3 (CH2 )8 SH] molecules allows
for developing the samples in a simple wet-etching process [13, 18, 22]. After depositing a self-assembled monolayer (SAM) of nonanethiol, the samples are exposed to the
atomic beam for eight minutes, corresponding to a dose of
about one metastable atom per SAM molecule. In a Penning ionization process, the SAM is locally damaged by the
metastable atoms [23]. After exposure, the samples are etched
in a cyanide solution that dissolves the damaged molecules,
and the underlying gold film [13, 18, 22]. The etching time is
also typically eight minutes. After etching, the sample topography is analyzed with an atomic force microscope (AFM).
3
Results
Figure 3 shows two 10 µm × 10 µm surface scans
of the samples taken with the AFM. The structure shown
in the left-hand image was created with a linearly polarized
optical mask. The dark regions indicate the positions where
the metastable helium atoms have hit the sample surface and
where the gold layer has been removed in the etching process.
The average structure height
√ is about 20 nm. The image shows
a lattice of dots with a λ/ 2 = 766 nm separation. The holes
have an average full width at half maximum (FWHM) diameter of 260 nm. The right-hand image pattern was produced
PETRA et al.
Atom lithography with two-dimensional optical masks
281
FIGURE 3 AFM surface scans of the samples. The images cover an area of
10 µm × 10 µm. The left-hand and right-hand images show the results of the
linearly polarized and the circularly polarized optical
√mask respectively. The
separation between both the lines and the dots is λ/ 2 = 766 nm
with a circularly polarized optical mask. The orientation of
the lines is perpendicular
to the mirror surface, and the line
√
separation is also λ/ 2, with an average diameter of 360 nm.
A close look at the structures shows a graininess typical for all
lithography experiments with gold layers [9, 13, 18]. Zooming in on a part of the figure shows that the gold typically
consists of approximately 20 nm diameter grains.
4
Discussion
For a better understanding of the created structures,
calculations of both the optical potential of the light field and
the expected atomic distributions on the samples have been
performed. The potentials of the optical masks corresponding to the intensity profiles of Fig. 1 are shown in Fig. 4a for
linearly polarized light (left-hand image) and circularly polarized light (right-hand image). The images cover an area
of 2λ × 2λ, where λ = 1083 nm is the wavelength of the optical transition. The gray-scale indicates the height of the
potential, where the lightest regions correspond to the areas
where the potential is the highest. For both polarizations, numerical simulations have been performed on the atoms that
travel through the 2D standing-wave light field. These calculations were done using the dipole force F(r) from (2) in
a three-dimensional model that calculates the atomic trajectories numerically. In a previous paper we have described this
model in detail [24]. The atomic distributions corresponding
to the potential plots are shown in Fig. 4b, where every black
dot represents the position where an atom has hit the sample.
As an initial distribution, a lattice of 201 × 201 atoms is used,
distributed homogeneously on a 4λ × 4λ grid. Both the longitudinal and transverse velocity of every atom is picked randomly from a Gaussian velocity distribution that corresponds
to the experimental values. The calculations, simulations and
measurements in Fig. 4 were taken at a sample position of
100 µm behind the center of the laser beam, in the downstream
direction of the atomic beam. From Fig. 4a and b it is clear that
the atoms are guided to the regions of the lowest potential, i.e.,
the dark regions of the potential plots. The calculated structure
for linearly polarized light (along the z -direction) shows
√ a grid
structure of the atoms, with a line separation of λ/ 2. For
the circularly polarized light field, a dotted pattern is√formed,
where the separation of two successive dots is λ/ 2 at an
angle of 45◦ with the x axis.
FIGURE 4 Calculations of the potential (a) , the atomic distributions on the
sample (b) and the experimental results (c) for a circularly polarized light
field (left-hand images) and linearly polarized light field (right-hand images).
All images cover an area of 2λ × 2λ, with λ the wavelength of the light
For comparison, the experimental results for both polarizations are shown in Fig. 4c as well. These images are closeups of a part (2λ × 2λ) of the images shown in Fig. 3. The images with a linearly polarized light field are in agreement with
the simulated atomic distribution shown in Fig. 4b. The qualitative visual agreement between the patterns is confirmed by
a 2D Fourier analysis of the distribution. The calculated diameter (FWHM) of the dots (along the x and y axis) is 170 nm,
which is in agreement with the measured width of 260 nm.
The broadened feature size seen in the experimental results
can be attributed to the isotropic etch process, that removes
the unprotected gold from all directions. The lack of visibility of the lines connecting the dots is probably because the
dose of metastable atoms was too small to damage the resist
layer enough in those specific areas. A longer exposure time,
however, will broaden the dots, similar to the 1D case [13].
The pattern formed with a circularly polarized light field
deviates strongly from the calculated structure. Instead of
a lattice of dots, the experimental results show a line pattern
orientated perpendicular to the upper standing-wave mirror
surface. We have considered a number of possible errors in either the experiment or the calculations that might explain the
deviation.
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Applied Physics B – Lasers and Optics
Experimentally, the simplest possible cause of producing
lines despite the square symmetry in the potential pattern is
the misalignment of the atomic beam with respect to the light
field. A large transverse velocity along one axis will lead to
potential averaging in that direction, suppressing structures.
However, simulations of this effect indicate that the required
misalignment angle is far outside of the experimental tolerances. Furthermore, the misalignment would correspond to
a rotation around a non-rotatable, mechanically fixed axis of
the sample holder.
The orientation of the tilt of the nonanethiol molecules on
the substrate might introduce locally an anisotropy on the surface. This could lead to a preferred direction for the etching
process. Although we cannot rule this effect out, it is difficult
to imagine how this could so drastically effect the structures
on the surface. Furthermore, such an effect would – at random
– have effected all measurements.
Local imperfections in the light field could lead to small
areas with a different symmetry in the light field intensity.
However, thorough examination of the samples with the AFM
have shown that the line pattern seen in Fig. 3 is clearly visible in a large area of 300 µm × 300 µm. Outside this area the
1D standing wave dominates the interference pattern, resulting in line structures with a separation of λ/2, and indicating
that the 2D structure is produced at the center of the 2D light
field. This
√ is confirmed by the structure direction and spacing (λ/ 2), that can only be explained from the atom having
experienced the force of a 2D optical mask.
Although the 2D standing wave is realized in a rigid sample holder by retro-reflecting a single laser beam (see Fig. 2)
it is not impossible that the interference pattern would smear
out partially during the eight to ten minutes exposure time of
the sample to the atomic beam by, e.g., thermal expansion of
the sample holder. As the sample is mounted in direct contact
with the first mirror, the most likely parameter to drift is the
distance between the two mirrors. We have simulated this effect by calculating the potential for different distances. This
indeed leads to a fluctuating phase difference between the interfering beams, but this does not affect the symmetry of the
pattern. Also, in the linear polarization case we have not seen
an effect of this sort.
A number of approximations can be identified in the calculations. The dipole potential of (1) is not strictly valid. First, it
is based on a steady-state approximation that is not well justified: the interaction time of the atoms with the light field is
not more than approximately twice the lifetime of the upper
state of the transition. Second, the magnetic degeneracy of the
J = 1 lower state leads to multiple potentials instead of a single one. In a more accurate approach, the actual (adiabatic)
dressed-state potentials have been calculated by diagonalizing
the interaction with the light field. These potentials are valid in
the short-interaction-time limit and take the magnetic substate
degeneracy into account. The two different dressed-state potentials (of which one is twofold degenerate) are proportional
to each other with a ratio of 4 : 3 for both linear and circular
polarization. The average potential corresponds closely to the
simple dipole potential close to the nodes of the light field, but
does not saturate near the antinodes. However, the symmetry
of the potential pattern is unaffected and remains square. This
also holds not only for linear and circular polarization of the
incoming beam, but also for arbitrary polarization of the incoming light beam and arbitrary polarization phase error of
the mirrors.
Non-adiabatic transitions of the atoms between the two
adiabatic potentials during their trajectories through the light
field could also influence the deposited pattern. However, the
adiabaticity condition ∆E ∆T 1/h (with ∆E the difference between the two adiabatic potentials and ∆T the interaction time) is satisfied by several orders of magnitude except
extremely close to the nodes in the light field. In a 2D configuration, non-adiabatic transitions can therefore be neglected.
Summarizing, we have not been able to find a satisfactory
explanation for the observed structures with a circularly polarized light field.
5
Conclusion
We have demonstrated atom lithography with
metastable helium using 2D optical masks. Calculations can
only partly explain the observed structures. With a linearly polarized light field a lattice of holes with a diameter (FWHM)
of 260 nm is created. The structures obtained with a circularly
polarized optical mask show lines in a direction perpendicular
to the mirror surface with a FWHM of 360 nm√. The separation between both the lines and the holes is λ/ 2 = 766 nm.
The structure size that may be written with 1083 nm light
in a 2D mask is determined by the wavelength of the light.
Structures with a smaller periodicity and size are feasible
when shorter wavelength light is used. In this respect the
2 3 S1 → 3 3 P2 transition is promising. Light at the λ = 389 nm
wavelength can be generated efficiently by frequency doubling of a Ti : sapphire laser [25]. The recent advent of diode
lasers at this wavelength is promising as well. However, the
problem with the 20 nm graininess of the structures remains,
and has to be solved when structures smaller than 20 nm are
aimed for.
ACKNOWLEDGEMENTS We are grateful to E.W.J.M. van
der Drift (DIMES Nanofacility, The Netherlands) for providing the silicon
wafers. Financial support from the Foundation for Fundamental Research on
Matter (FOM) is gratefully acknowledged.
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